Method for studying a zone of an object so as to determine a mass-thickness and a composition thereof by using an electron beam and measurements of x-ray radiation intensity

ABSTRACT

A method for studying a zone of an object, the zone exhibiting a mass-thickness and comprising at least one chemical element, the method including a step of exposing a part of the zone of the object to an electron beam, a step of identifying each chemical element present in the said zone by virtue of the exposure step, a step of measuring, for each chemical element identified, a corresponding intensity of an X-ray radiation emergent from the object on account of the said exposure step, a step of determining a value of the said mass-thickness dependent on each measurement step, and a step of determining a value of the concentration of each chemical element identified using the said value of the mass-thickness determined.

TECHNICAL FIELD OF THE INVENTION

The invention relates to the field of object study, for example by energy dispersive or wavelength dispersive spectrometry in an electron microscope, of which it is sought to characterize a zone by determining its mass-thickness and its composition in terms of chemical element(s).

The subject of the invention is more particularly a method for studying a zone of the object, the said zone exhibiting a mass-thickness and comprising at least one chemical element. The method of study accordingly uses in particular an electron beam and X-ray radiation intensity measurements deriving from the interaction of the beam with the said zone.

PRIOR ART

To determine the composition of a wafer made of a material, in particular homogeneous, it is known to use measurements based on energy dispersive or wavelength dispersive spectrometry using, for example, scanning electron microscopes (SEM) or transmission electron microscopes (TEM).

A first known scheme is limited to studying an object, for example taking the form of a wafer as mentioned hereinabove, whose thickness is such that the electron beam interacting with the said object is entirely absorbed by the said object. It is then assumed that the thickness of the wafer is infinite.

A second known scheme is limited to studying an object, for example taking the form of a wafer as mentioned hereinabove, which is totally transparent to the electron beam used during the study. It is then assumed that the thickness of the wafer is zero.

These two schemes give approximate but unsatisfactory results. In particular, these results are erroneous when the thickness of the object is such that part of the electron beam is transmitted by the said object.

OBJECT OF THE INVENTION

The aim of the present invention is to propose a solution making it possible to take into account the thickness of the object over the zone studied.

This aim is addressed by virtue of a method for studying a zone of an object, the said zone exhibiting a mass-thickness and comprising at least one chemical element, the said method comprising:

-   -   a step of exposing a part of the zone of the object to an         electron beam,     -   a step of identifying each chemical element present in the said         zone by virtue of the exposure step,     -   a step of measuring, for each chemical element identified, a         corresponding intensity of an X-ray radiation emergent from the         object on account of the said exposure step,     -   a step of determining a value of the said mass-thickness         dependent on each measurement step,     -   a step of determining a value of the concentration of each         chemical element identified using the said value of the         mass-thickness determined.

The method also comprises an initialization step in which an intermediate value of the mass-thickness ρz₀, with ρ the assumed density and z₀ the assumed thickness of the object at the level of the said zone, and an intermediate value of concentration C_(ic) of each chemical element identified are determined by choice, especially by considering that the intensity of the corresponding emergent X-ray radiation is equal to the intensity of the radiation generated in the object by the said corresponding chemical element, and the method comprises an iterative cycle of steps comprising for each iteration of the said cycle:

-   -   a step of calculating an incidence correction term Θ intended to         take account of the angle of incidence θ of the electron beam         and associated with the zone studied,     -   a fitting step, implemented for each chemical element         identified, and comprising:         -   a step of calculating an incidence correction term Θ _(im)             associated with the said chemical element identified and             intended to take account of the angle of incidence θ of the             electron beam,         -   a step of calculating an atomic number correction term φ             _(i) for the said corresponding chemical element using the             incidence correction terms Θ and Θ _(im) calculated in the             course of the said cycle,         -   a step of calculating an absorption correction term χ _(i)             for the said corresponding chemical element using the             incidence correction terms Θ and Θ _(im) calculated in the             course of the said cycle, and the atomic number correction             term φ _(i) calculated in the course of the said cycle,     -   a step of modifying the intermediate value of mass-thickness ρz₀         using the incidence correction term Θ calculated in the course         of the said cycle, and the incidence correction Θ _(im), atomic         number correction φ _(i) and absorption correction χ _(i) terms         calculated in the course of the said cycle for each chemical         element and dependent on each measurement step,     -   a step of modifying, for each chemical element, the intermediate         value of concentration C_(ic) of the said corresponding chemical         element using the intermediate value of mass-thickness ρz_(o) as         modified in the course of the said cycle, the incidence         correction term Θ calculated in the course of the said cycle and         the incidence correction Θ _(im), atomic number correction φ         _(i) and absorption correction χ _(i) terms calculated in the         course of the said cycle and corresponding to the said chemical         element,         and the iteration is halted when the variation, between two         successive iterations of the intermediate values of         mass-thickness ρz₀ and of the intermediate values of         concentration C_(ic) of each chemical element, is less than an         associated predetermined threshold, the said modified         intermediate mass-thickness value defining the mass-thickness         value determined and each modified intermediate concentration         value defining the corresponding concentration value determined.

According to one embodiment, each step of calculating the incidence correction term Θ comprises the solving of the following equation:

${\text{-}\overset{\_}{\Theta}} = \left\{ {1 + {\left\lbrack {{\frac{\rho \; z_{0}}{\cos \; \theta}{f\left( _{c} \right)}} - {2\frac{\cos \; \theta}{\rho}\left( {1 - ^{14{({1 - \rho})}\frac{\rho \; z_{0}}{\cos \; \theta}{f{(_{c})}}}} \right)^{{- 2}\frac{\rho \; z_{0}}{\cos \; \theta}{f{(_{c})}}}}} \right\rbrack \left\lbrack {\frac{1}{\cos \; \theta} - 1} \right\rbrack}} \right\}^{0.6}$

-   -   and each step of calculating the incidence correction term Θ         _(im) comprises the solving of the following equation:

${\text{-}{\overset{\_}{\Theta}}_{im}} = \left\{ {1 + {\left\lbrack {{\frac{\rho \; z_{im}}{\cos \; \theta}{f_{m}\left( E_{is} \right)}} - {2\frac{\cos \; \theta}{\rho}^{{- 2}\frac{\rho \; z_{im}}{\cos \; \theta}{f_{m}{(E_{is})}}}}} \right\rbrack \left\lbrack {\frac{1}{\cos \; \theta} - 1} \right\rbrack}} \right\}^{0.6}$

with

_(c) the mean atomic number of the object at the level of the said zone, ƒ(

_(c)) a function of the mean atomic number

_(c), z_(im) the maximum ionization depth of the corresponding chemical element, ƒ_(m)(E_(is)) a function of the ionization threshold energy E_(is) of the energy level considered of a corresponding chemical element.

For example, we have

f(Z−_(c)) = ^(a(LnZ−_(c))⁴ + b(LnZ−_(c))³ + c(LnZ−_(c))² + d LnZ−_(c)+e ),

with a, b, c, d, e parameters determined by Monte-Carlo simulation and depending on the energy of the electrons of the said electron beam.

In particular,

${f_{m}\left( E_{is} \right)} = \frac{{AE}_{is}^{m}}{\left( {R_{p}\text{/}S_{p}} \right)_{i}}$

with (R_(p)/S_(p))_(i) being the ratio of the backscattering coefficients R_(p) and of the stopping power S_(p) for the corresponding pure chemical element, and A and m parameters determined by Monte-Carlo simulation and depending on the energy level for the said corresponding chemical element.

According to one embodiment, each step of calculating the atomic number correction term φ _(i) uses the following relation

${{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{\theta}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{\theta}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{\theta}} \right)^{n}}} \right)}}}$

with I_(igco) the intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the said electron beam, ξ_(i) the zeta-factor associated with the said corresponding chemical element, n a parameter depending on the mean atomic number Zc of the object at the level of the said zone, α a parameter depending on the mean atomic number Zc of the object at the level of the said zone, β_(i) a term making it possible to fit the maximum of the term φ _(i) and z_(θ) the thickness in the direction of incidence θ determined on the basis of the incidence correction terms Θ and Θ _(im) calculated in the course of the said cycle.

For example, the parameter n is determined by the following relation n=n₁ Ln

_(c)+n₂, the parameters n₁ and n₂ being given by a chart giving the value of n as a function of

_(c) whatever the power of the electron beam.

For example, the parameter α is determined by the following relation

α = ^((α₁(LnZ−_(c))² + α₂LnZ−_(c)+α₃))

with α₁, α₂ and α₃ parameters depending on the initial energy E₀ of the electrons of the electron beam.

According to one embodiment, the term β_(i) is determined by supposing that, for any thickness greater than or equal to a maximum ionization depth z_(im) of the corresponding chemical element, the intensity of the X-ray radiation generated in the object is equivalent to that of the object if the latter is opaque to the said electron beam.

In particular, according to the said embodiment, the term β_(i) is obtained by solving the following equation:

$\beta_{i} = \left\{ {\begin{matrix} {{\left( {\rho \; z_{im}} \right)^{n}\frac{\left( {{\frac{\xi_{i}}{C_{ic}}\frac{I_{igco}}{\rho \; z_{im}}} - 1} \right)}{{\alpha \left( {\rho \; z_{im}} \right)}^{n} - \left( {{\frac{\xi_{i}}{C_{ic}}\frac{I_{igco}}{\rho \; z_{im}}} - 1} \right)}},} & {{{if}\mspace{14mu} \beta_{i}} > 0} \\ {0,} & {{{if}\mspace{14mu} \beta_{i}} \leq 0} \end{matrix},} \right.$

with z_(im) the maximum ionization depth of the corresponding chemical element.

According to an implementation, each step of calculating the absorption correction term χ _(i) makes use of solving the equation

${\overset{\_}{\chi}}_{i} = \left\{ \begin{matrix} {\frac{\chi_{ic}\rho \; z_{0}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}}{\begin{matrix} {{\phi_{i}(0)} + \frac{P_{i}}{\chi_{ic}} + \left\{ {{P_{i}^{\prime}\left( {\frac{1}{\chi_{ic}} - {\rho \; z_{0}}} \right)} - \left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}}{\chi_{ic}}} \right\rbrack + {\left( {P_{i}^{\prime} - P_{i}} \right)\rho \; z_{ib}}} \right\}} \\ {^{{- \chi_{ic}}\rho \; z_{ib}} - {\left\lbrack {{\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}^{\prime}}{\chi_{ic}}} \right\rbrack ^{{- \chi_{ic}}\rho_{z_{0}}}}} \end{matrix}},} & {{{if}\mspace{14mu} z_{ib}} > 0} \\ {\frac{\rho \; z_{0}\chi_{ic}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}}{{\phi_{i}(0)} + \frac{P_{i}^{''}}{\chi_{ic}} - {\left\{ {{P_{i}^{''}\left( {\frac{1}{\chi_{ic}} + {\rho \; z_{0}}} \right)} + {\phi_{i}(0)}} \right\} ^{{- \chi_{ic}}\rho \; z_{0}}}},} & {{{if}\mspace{14mu} z_{ib}} \leq 0} \end{matrix} \right.$

with φ_(i)(0) the value of the distribution of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element, φ_(i)(ρz₀) the value of the distribution of the intensities of the X-ray radiation generated at the depth z₀ of the object by the corresponding chemical element, P_(i) the initial slope of the distribution of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element and determined by the relation

$P_{i} = {\frac{g \cdot h^{4} \cdot \left( {F\text{/}\overset{\_}{R}} \right)^{2}}{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{i\; \theta}} \right)}\rho \; z_{i\; \theta}}\frac{1}{\left( {\cos \; \theta} \right)^{4}}\mspace{14mu} {with}}$ ${{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{i\; \theta}} \right)} = {{\frac{1 + {\alpha \left( {\rho \; z_{\theta}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{\theta}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{\theta}} \right)^{n}}} \right)}}}\mspace{14mu} {and}\mspace{14mu} z_{i\; \theta}} = \frac{z_{im}}{{\overset{\_}{\Theta}}_{im}\cos \; \theta}}},$

χ_(ic) representing the mass absorption coefficient of the compound for the characteristic X-ray radiation of the corresponding chemical element, φ _(i)(ρz_(θ)) being the atomic number correction term calculated in the course of the said cycle,

${P_{i}^{\prime} = \frac{\left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack^{2} + {2P_{i}\rho \; {z_{0}\left\lbrack {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack}}}{\rho \; {z_{0}\left\lbrack {{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}} - {2{\phi_{i}(0)}} - {P_{i}\rho \; z_{0}}} \right\rbrack}}},{P_{i}^{''} = {2\frac{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} - {\phi_{i}(0)}}{\rho \; z_{0}}}},{z_{ib} = {z_{0}\frac{{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}} - {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}{{P_{i}\rho \; z_{0}} + {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}}},$

z_(im) the maximum ionization depth of the corresponding chemical element, β_(i) a term making it possible to fit the maximum of the atomic number correction term, I_(igco) the intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the said electron beam, ξ_(i) the zeta-factor associated with the said corresponding chemical element, α a parameter depending on the mean atomic number Zc of the object at the level of the said zone, n a parameter depending on the mean atomic number Zc of the object at the level of the said zone and z_(θ) the depth of the object at the level of the said zone while taking account of the incidence θ of the electron beam.

In particular, the parameter φ_(i)(0) can be calculated in the following manner:

$\mspace{20mu} {{\phi_{i}(0)} = \left\{ {{{\begin{matrix} {{1 + {\left\lbrack {{\phi_{im}(0)} - 1} \right\rbrack \frac{z_{0}}{{\overset{\_}{z}}_{i}}}},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i}} \\ {{\phi_{im}(0)},} & {{{if}\mspace{14mu} z_{0}} \geq {\overset{\_}{z}}_{i}} \end{matrix}\mspace{14mu} {with}{\overset{\_}{z}}_{i}} = {{\overset{\_}{z}}_{ip}\frac{\rho_{i}}{\rho}{\frac{n}{n_{i}}\left\lbrack {1 + {0.048\left( {2.5 - \frac{E_{0}}{20}} \right)\left( {1 - {LnM}_{i} + \frac{\left( {LnM}_{i} \right)^{2}}{3}} \right)\left( {\frac{M_{c}}{M_{i}} - 1} \right)}} \right\rbrack}}},} \right.}$

φ_(i)(0) the surface ionization of the corresponding chemical element in the object considered to be opaque to the said electron beam, z _(ip) the thickness for which the atomic number correction term φ _(i) for the corresponding pure chemical element is a maximum, n and n_(i) parameters depending respectively on the mean atomic number of the object and on the atomic number of the pure chemical element, ρ_(i) the density of the corresponding pure chemical element and M_(c) and M_(t) the atomic masses of the object and of the corresponding pure chemical element, and E₀ the initial energy of the electrons of the electron beam.

The method can comprise a step of determining a parameter z _(iθ) corresponding to the minimum value between z _(i) and z_(iθ) and defined by the following relation: z _(iθ)=Min(z _(i),z_(iθ)).

In particular, the term φ_(i)(ρz₀) is determined in the following manner:

${\phi_{i}\left( {\rho \; z_{0}} \right)} = \left\{ {\begin{matrix} {{\left\{ {{\left\lbrack {\frac{3}{2} - {\phi_{i}(0)}} \right\rbrack {\frac{z_{0}}{{\overset{\_}{z}}_{i\; \theta}}\left\lbrack {2 - \frac{z_{0}}{{\overset{\_}{z}}_{i\; \theta}}} \right\rbrack}} + {\phi_{i}(0)}} \right\} \cos \; \theta},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i\; \theta}} \\ {{{\frac{3}{2}\left\{ {{\left\lbrack \frac{z_{0} - {\overset{\_}{z}}_{i\; \theta}}{z_{im} - {\overset{\_}{z}}_{i\; \theta}} \right\rbrack \left\lbrack {\frac{z_{0} - {\overset{\_}{z}}_{i\; \theta}}{z_{im} - {\overset{\_}{z}}_{i\; \theta}} - 2} \right\rbrack} + 1} \right\}} + {\cos \; \theta}},} & {{{if}\mspace{14mu} {\overset{\_}{z}}_{i\; \theta}} \leq z_{0} \leq z_{im}} \\ 0 & {{{if}\mspace{14mu} z_{0}} > z_{im}} \end{matrix}.} \right.$

According to a variant, the angle of incidence θ being zero then the two incidence correction terms Θ and Θ _(im) are equal to 1 so that the atomic number correction term is determined on the basis of the following equation

${{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{0}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{0}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{0}} \right)^{n}}} \right)}}}$

with I_(igco) the intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the said electron beam, ξ_(i) the zeta-factor associated with the said corresponding chemical element, n a parameter depending on the mean atomic number Zc of the object at the level of the said zone, α a parameter depending on the mean atomic number Zc of the object at the level of the said zone, β_(i) a term making it possible to fit the maximum of the term φ _(i), and in that

${\overset{\_}{\chi}}_{i} = \left\{ {{\begin{matrix} {\frac{\chi_{ic}\rho \; z_{0}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}}{\begin{matrix} {{\phi_{i}(0)} + \frac{P_{i}}{\chi_{ic}} + \left\{ {{P_{i}^{\prime}\left( {\frac{1}{\chi_{ic}} - {\rho \; z_{0}}} \right)} - \left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}}{\chi_{ic}}} \right\rbrack + {\left( {P_{i}^{\prime} - P_{i}} \right)\rho \; z_{ib}}} \right\}} \\ {^{{- \chi_{ic}}\rho \; z_{ib}} - {\left\lbrack {{\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}^{\prime}}{\chi_{ic}}} \right\rbrack ^{{- \chi_{ic}}\rho \; z_{0}}}} \end{matrix}},} & {{{if}\mspace{14mu} z_{ib}} > 0} \\ {\frac{\rho \; z_{0}\chi_{ic}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}}{{\phi_{i}(0)} + \frac{P_{i}^{''}}{\chi_{ic}} - {\left\{ {{P_{i}^{''}\left( {\frac{1}{\chi_{ic}} + {\rho \; z_{0}}} \right)} + {\phi_{i}(0)}} \right\} ^{{- \chi_{ic}}\rho \; z_{0}}}},} & {{{if}\mspace{14mu} z_{ib}} \leq 0} \end{matrix}\mspace{20mu} {with}\mspace{20mu} {\phi_{i}\left( {\rho \; z_{0}} \right)}} = \left\{ {\begin{matrix} {{{\left\lbrack {\frac{3}{2} - {\phi_{i}(0)}} \right\rbrack {\frac{z_{0}}{{\overset{\_}{z}}_{i\;}}\left\lbrack {2 - \frac{z_{0}}{{\overset{\_}{z}}_{i\;}}} \right\rbrack}} + {\phi_{i}(0)}},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i\;}} \\ {{\frac{3}{2}\left\{ {{\left\lbrack \frac{z_{0} - {\overset{\_}{z}}_{i\;}}{z_{im} - {\overset{\_}{z}}_{i\;}} \right\rbrack \left\lbrack {\frac{z_{0} - {\overset{\_}{z}}_{i\;}}{z_{im} - {\overset{\_}{z}}_{i\;}} - 2} \right\rbrack} + 1} \right\}},} & {{{if}\mspace{14mu} {\overset{\_}{z}}_{i}} \leq z_{0} \leq z_{im}} \\ 0 & {{{if}\mspace{14mu} z_{0}} > z_{im}} \end{matrix},} \right.} \right.$

φ_(i)(0) the value of the distribution of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element, P_(i) the initial slope of the distribution of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element and determined by the relation

${P_{i} = {{\frac{g \cdot h^{4} \cdot \left( {F\text{/}\overset{\_}{R}} \right)^{2}}{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{im}} \right)}\rho \; z_{im}}\mspace{14mu} {with}\mspace{14mu} {{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{im}} \right)}} = \frac{1 + {\alpha \left( {\rho \; z_{im}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{im}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{im}} \right)^{n}}} \right)}}}}},$

χ_(ic) representing the mass absorption coefficient of the object for the corresponding chemical element

${P_{i}^{\prime} = \frac{\left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack^{2} + {2P_{i}\rho \; {z_{0}\left\lbrack {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack}}}{\rho \; {z_{0}\left\lbrack {{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}} - {2{\phi_{i}(0)}} - {P_{i}\rho \; z_{0}}} \right\rbrack}}},{P_{i}^{''} = {2\frac{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} - {\phi_{i}(0)}}{\rho \; z_{0}}}},{and}$ ${z_{ib} = {z_{0}\frac{{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}} - {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}{{P_{i}\rho \; z_{0}} + {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}}},$

z_(im) the maximum ionization depth of the corresponding chemical element,

${{\overset{\_}{z}}_{i} = {{\overset{\_}{z}}_{ip}\frac{\rho_{i}}{\rho}{\frac{n}{n_{i}}\left\lbrack {1 + {0.048\left( {2.5 - \frac{E_{0}}{20}} \right)\left( {1 - {LnM}_{i} + \frac{\left( {LnM}_{i} \right)^{2}}{3}} \right)\left( {\frac{M_{c}}{M_{i}} - 1} \right)}} \right\rbrack}}},$

z _(ip) the thickness for which the atomic number correction term φ_(i) for the corresponding pure chemical element is a maximum, n and n_(i) parameters depending respectively on the mean atomic number of the object and on the atomic number of the corresponding pure element, ρ_(i) the density of the corresponding pure chemical element and M_(c) and M_(t) the atomic masses of the object and of the corresponding pure chemical element, E₀ the initial energy of the electrons of the electron beam, β_(i) a term making it possible to fit the maximum of the atomic number correction term, I_(igco) the intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the said electron beam, ξ_(i) the zeta-factor associated with the said corresponding chemical element, α a parameter depending on the mean atomic number Zc of the object at the level of the said zone (Z1), n a parameter depending on the mean atomic number Zc of the object at the level of the said zone.

Preferentially, in the course of each cycle the intermediate value of the mass-thickness is modified according to the following formula

${\rho \; z_{0}} = {\overset{\_}{\Theta}\; \cos \; \theta {\sum\limits_{i = 1}^{N}{\xi_{i}\frac{{\overset{\_}{\chi}}_{i}I_{iec}}{{\overset{\_}{\phi}}_{i}}}}}$

with N the total number of chemical elements identified, i the index of the current chemical element studied, I_(iec) the intensity of the emergent X-ray radiation corresponding to the said chemical element of index i, χ _(i) the absorption correction term calculated in the course of the said cycle and corresponding to the said chemical element of index i, ξ_(i) the zeta-factor associated with the said chemical element of index i, the atomic number correction term φ _(i) calculated in the course of the said cycle and corresponding to the said chemical element of index i, Θ the incidence correction term calculated in the course of the said cycle.

Preferentially, in the course of each cycle the intermediate value of concentration C_(ic) of each chemical element is calculated according to the following formula:

$C_{ic} = {\frac{\xi_{i}}{\rho \; z_{0}}\frac{{\overset{\_}{\chi}}_{i}I_{iec}}{{\overset{\_}{\phi}}_{i}}\overset{\_}{\Theta}\; \cos \; \theta}$

with I_(iec) the measured intensity of the emergent X-ray radiation of the said corresponding chemical element, ρz₀ the intermediate mass-thickness value modified in the course of the said cycle, χ _(i) the absorption correction term for the said corresponding chemical element calculated in the course of the said cycle, ξ_(i) the zeta-factor associated with the said corresponding chemical element, the atomic number correction term φ _(i) calculated in the course of the said cycle for the said corresponding chemical element, Θ the incidence correction term calculated in the course of the said cycle.

The invention also relates to a method for studying an object comprising the following steps:

-   -   Dividing the object into several zones to be studied,     -   Implementing, for each zone, the hereinabove described method         for studying the zone, with a view to determining the         corresponding mass-thickness value and, for each element of the         said zone, the corresponding concentration value.

SUMMARY DESCRIPTION OF THE DRAWINGS

Other advantages and characteristics will emerge more clearly from the description which follows of particular embodiments of the invention which are given by way of nonlimiting examples and represented in the appended drawings, in which:

FIG. 1 schematically illustrates various steps of a method of study according to a mode of execution of the invention,

FIG. 2 is a schematic view of the interaction of an electron beam with an object,

FIG. 3 illustrates various steps of the method of study,

FIG. 4 illustrates a way of determining parameters of a function ƒ(

_(c)) by Monte-Carlo simulation,

FIG. 5 illustrates a way of determining parameters of a function ƒ_(m)(E_(is)) by Monte-Carlo simulation, the said parameters depending on the emission level K, L or M,

FIG. 6 illustrates the variation of the parameter n as a function of the mean atomic number Zc for various powers of the electron beam,

FIG. 7 illustrates the variation of the parameter α as a function of the mean atomic number Zc for various powers of the electron beam,

FIG. 8 is a simulation of the atomic number correction term φ _(i) dependent on the total thickness of an object in the form of a wafer, the points are calculated by using intensities of the X-ray radiation generated by Monte-Carlo simulation and the dashed curves represent what it is possible to obtain by using the model of the method of study according to a mode of execution of the invention.

DESCRIPTION OF PREFERENTIAL MODES OF THE INVENTION

The method described hereinafter for studying a zone differs from the prior art in that the thickness of the object to be studied will be determined (that is to say not considered to be zero or infinite).

In this sense, the invention relates to a method for studying a zone of an object, the said zone exhibiting a mass-thickness and comprising at least one chemical element. The chemical element(s) will be identified in the course of the method of study. In particular, in the present description, when one speaks of a chemical element, this refers to an identified chemical element.

In the present description, “chemical element” is understood to mean an element of the periodic classification of the elements.

Generally, in the present description, when a term or a parameter comprises the index i, it is considered that this refers to a term or a parameter related to the said chemical element corresponding to this index i, i then ranging from 1 to N with N the total number of chemical elements identified.

The object can be a wafer of constant or variable thickness.

As illustrated in FIG. 1, the method of study comprises a step E1 of exposing a part of the zone of the object to an electron beam. Preferably, in contradistinction to the prior art, this exposure step is carried out in such a way that the electron beam is partially transmitted by the object.

FIG. 2 illustrates an example in which a beam 1 of electrons of energy E₀ interacts with the said part of the zone Z1 studied of the object 2 according to an angle of incidence 8. This angle of incidence 8 is given according to the normal with respect to the exterior surface of the object 2, impacted by the electron beam 1. In particular, in FIG. 2, a part of the electron beam 1 is transmitted by the object 2. The interaction of the electron beam 1 with the part of the zone Z1 results in the generation of additional X-ray radiations which will propagate in the zone studied. In particular, each chemical element i present in the zone studied will generate an X-ray radiation of intensity I_(igc) which will propagate in the zone studied and part of which will be absorbed by the chemical element i of the zone and another part of which will be transmitted out of the object so as to form an emergent X-ray radiation I_(iec). It is therefore understood why the zone studied is more significant than the part of the zone interacting directly with the electron beam 1.

It follows from what was stated hereinabove that when the electron beam exhibits an incidence of angle θ, this incidence is associated with a traversed thickness z_(θ) of the object which is in fact the thickness of the object along an axis according to which the electron beam extends. The angle θ is given between the axis of the electron beam and the normal at the level of the point of impact of the electron beam on the object. This thickness z_(θ) is greater than the real thickness of the object z₀ which is itself given according to the normal of the exterior surface of the object. This thickness z_(θ) can further be defined as the depth of the object at the level of the said zone studied while taking account of the incidence θ of the electron beam.

The method of study furthermore comprises a step E2 of identifying each chemical element present in the said zone Z1 by virtue of the exposure step E1. In fact, by using spectrometry techniques giving a number of ticks per second as a function of the energy, it is possible to ascertain which chemical elements are present in the zone Z1 concerned of the object 2. The general composition is then known at the level of the zone Z1 but without knowing the corresponding percentages. This may, for example, be implemented by energy dispersive spectrometry especially in a scanning electron microscope.

In this sense, the method for studying the zone Z1 will seek to determine the mass-thickness of the object 2 at the level of the zone studied Z1 and then to determine the concentration of each chemical element identified. Accordingly, the method for studying the zone Z1 of the object 2 comprises a step E3 of measuring, for each chemical element identified, a corresponding intensity of an X-ray radiation I_(iec) emergent from the object 2 on account of the said exposure step, a step E4 of determining a value of the said mass-thickness dependent on each measurement step, and a step E5 of determining a value of the concentration of each chemical element identified using the said value of the mass-thickness determined.

The measurement of each intensity of the emergent X-ray radiation I_(iec) is in particular carried out by energy dispersive or wavelength dispersive spectrometry.

The expression “value of the mass-thickness determined” is understood to mean a value of the real mass-thickness of the object that is obtained in particular by calculation.

It is therefore understood that the method for studying the zone Z1 of the object 2 makes it possible to take into account the mass-thickness within the framework of the determination of the concentration of each chemical element.

The scheme implemented in the present method of study making it possible to determine the value of the mass-thickness and the value of the concentration of each chemical element identified advantageously uses a principle of iterative approximation. In this sense, we shall choose, either in an arbitrary manner, or on the basis of assumptions, an intermediate value of mass-thickness and an intermediate value of concentration of each chemical element. Thereafter, these intermediate values are modified in an iterative manner by injections into suitable functions so as to obtain modified corresponding intermediate values. When the variation of the intermediate values between two successive iterations is less than a predetermined threshold, for example less than a variation of 0.1%, then it is considered that the real values of mass-thickness of the object and of concentration of the corresponding chemical elements are attained.

In a more detailed manner, the method of study can comprise an initialization step E6 (FIG. 3) in which an intermediate value of the mass-thickness ρz₀, with ρ the assumed density and z₀ the assumed thickness of the object 2 at the level of the said zone Z1, and an intermediate value of concentration C_(ic) of each chemical element identified are determined by choice. This step E6 is generally carried out between step E3 and step E4.

Preferably, the said choice for each chemical element identified of the intermediate value of concentration C_(ic) is made by considering that the intensity of the corresponding emergent X-ray radiation I_(iec) is equal to the intensity of the radiation I_(igc) generated in the object 2 by the said corresponding chemical element. The intermediate value of the mass-thickness ρz₀ can then also be determined as a function of this consideration.

More particularly, to calculate a mass-thickness ρz₀ subsequent use will be made of an incidence correction general term Θ and for each chemical element identified an incidence correction term Θ _(im) for the said corresponding chemical element, an atomic number correction term φ _(i) for the said corresponding chemical element and an absorption correction term χ _(i) for the said corresponding chemical element.

Thus, with reference to what was stated hereinabove, the choice can suppose as initial condition that the incidence correction general term Θ (calculated for the compound, that is to say the zone of the object), and the atomic number and absorption correction terms φ _(i) and χ _(i) for each constituent i are equal to 1. In this case we have for chosen intermediate value of the mass-thickness ρz₀:

ρz ₀=cos θΣ_(i=1) ^(N)ξ_(i) I _(iec)  (eq. 1)

With ξ_(i) the zeta-factor associated with the said corresponding chemical element, and I_(iec) the measured intensity of the emergent X-ray radiation for the said corresponding chemical element.

In the present description, the zeta-factor ξ_(i) is advantageously that as defined by Watanabe M. and Williams D. B. (2006) in “The quantitative analysis of thin specimens: a review of progress from the Cliff-Lorimer to the new ξ-factor methods, Journal of Microscopy”, vol. 221, p. 89-109, 2006. The zeta-factor ξ_(i) being in particular determined on the basis of a totally transparent wafer (φ _(i)=1) composed exclusively of the pure corresponding chemical element in the following manner:

$\begin{matrix} {\xi_{i} = {\lim_{{\rho \; z_{0}}\rightarrow 0}\frac{\rho \; z_{0}}{I_{igp}}}} & \left( {{eq}.\mspace{11mu} 2} \right) \end{matrix}$

With I_(igp) the intensity of the X-ray radiation generated by the corresponding pure chemical element, for example measured experimentally or simulated by means of a statistical model of Monte-Carlo type.

And we have for chosen intermediate value of concentration C_(ic) of the chemical element i:

$\begin{matrix} {C_{ic} = {\frac{\xi_{i}}{\rho \; z_{0}}I_{iec}\cos \; \theta}} & \left( {{eq}.\mspace{11mu} 3} \right) \end{matrix}$

with ρz₀ obtained on the basis of equation (eq. 1).

After the appropriate choice of the intermediate values of concentration C_(ic) and of the mass-thickness ρz₀ in the course of the initialization step E6, the method of study comprises an iterative cycle of steps E7 comprising, for each iteration of the said cycle E7, a step E7-0 of calculating the incidence correction term Θ intended to take account of the angle of incidence θ of the electron beam and associated with the zone Z1 studied. The cycle furthermore comprises, for each iteration, a fitting step E7-1, implemented for each chemical element identified. This fitting step E7-1 comprising a step E7-1-1 of calculating an incidence correction term Θ _(im) associated with the said chemical element identified and intended to take account of the angle of incidence θ of the electron beam 1.

Hereinafter, when one speaks of a term calculated in the course of the said cycle, one is speaking of that calculated in the course of the current iteration of the said cycle.

According to a particular example, the steps of calculating the two incidence correction terms Θ and Θ _(im) comprise respectively the solving of the following equations:

$\begin{matrix} {{\text{-}\overset{\_}{\Theta}} = {\quad{\quad {\quad \left\{ {1 + \left\lbrack {\frac{\rho \; z_{0}}{\cos \; \theta}f {\quad\left( {\left. \quad _{c} \right) - \left. \quad{2\frac{\cos \; \theta}{\rho}{\left. \quad {\left( {1 - ^{14{({1 - \rho})}\frac{\rho \; z_{0}}{\cos \; \theta}{f{(_{c})}}}} \right)^{{- 2}\frac{\rho \; z_{0}}{\cos \; \theta}{f{(_{c})}}}} \right\rbrack \left\lbrack {\frac{1}{\cos \; \theta} - 1} \right\rbrack}} \right\}^{0.6}} \right.}} \right.} \right.}}}} & \left( {{eq}.\mspace{11mu} 4} \right) \end{matrix}$

for step E7-0

$\begin{matrix} {{\text{-}{\overset{\_}{\Theta}}_{im}} = \left\{ {1 + {\left\lbrack {{\frac{\rho \; z_{im}}{\cos \; \theta}{f_{m}\left( E_{is} \right)}} - {2\frac{\cos \; \theta}{\rho}^{{- 2}\frac{\rho \; z_{im}}{\cos \; \theta}{f_{m}{(E_{is})}}}}} \right\rbrack \left\lbrack {\frac{1}{\cos \; \theta} - 1} \right\rbrack}} \right\}^{0.6}} & \left( {{eq}.\mspace{11mu} 5} \right) \end{matrix}$

for each step E7-1-1 with

_(c) the mean atomic number of the object at the level of the said zone, ƒ(

_(c)) a function of the mean atomic number

_(c), z_(im) the maximum ionization depth of the corresponding chemical element, ƒ_(m)(E_(is)) a function of the ionization threshold energy E_(is) of the energy level considered of a corresponding identified chemical element. Of course, it is clear that in equations (eq. 4) and (eq.5) the intermediate value of the mass-thickness ρz₀ is that at the time at which the corresponding step cycle is initiated (whether this be that chosen within the framework of the first iteration or that modified during the successive iterations).

More particularly, z_(im) is determined in a manner known by the person skilled in the art, in particular by applying:

$\begin{matrix} {z_{im} = \frac{64\left( {E_{0}^{1.68} - E_{is}^{1.68}} \right)}{\rho}} & \left( {{eq}.\mspace{11mu} 6} \right) \end{matrix}$

With E_(is) the ionization threshold energy of the energy level considered for the said corresponding chemical element (in keV).

According to a particular embodiment, we have:

$\begin{matrix} {{f\left( _{c} \right)} = ^{{a{({L\; n\; _{c}})}}^{4} + {b\; {({L\; n\; _{c}})}^{3}} + {c{({L\; n\; _{c}})}}^{2} + {d\; L\; n\; _{c}} + e}} & \left( {{eq}.\mspace{14mu} 7} \right) \end{matrix}$

with a, b, c, d, e parameters determined by Monte-Carlo simulation and depending on the energy of the electrons of the electron beam. In particular, FIG. 4 illustrates an example of determining the parameters of the function ƒ(

_(c)) by Monte-Carlo simulation for an energy E₀ of 30 kV. Thus, knowing E₀, it is easy to derive the parameters a, b, c, d which in the example of 30 kV are respectively equal to 0.0314, −0.4661, 2.2686, −3.8452 and −7.6463.

According to a particular embodiment, we have

$\begin{matrix} {{f_{m}\left( E_{is} \right)} = \frac{{AE}_{is}^{m}}{\left( {R_{p}/S_{p}} \right)_{i}}} & \left( {{eq}.\mspace{14mu} 8} \right) \end{matrix}$

with (R_(p)/S_(p))_(i) the ratio of the backscattering coefficients R_(p) and of the stopping power S_(p) for the corresponding pure chemical element, and A and m parameters determined by Monte-Carlo simulation and depending on the energy level considered for the said corresponding chemical element (the energy level corresponds to the electron shells of the atom excited by the electron beam). And with as seen previously E_(is) the ionization threshold energy of the energy level considered. FIG. 5 gives an example of determining the parameters of the function ƒ_(m)(E_(is)) by Monte-Carlo simulation, the parameters of the function depending on the energy level considered and dependent on the electron shells K, L or M excited by the electron beam.

It should be noted that in the present description, if at the time of a calculation z₀≧z_(im), then the thickness z₀ is modified in such a way that it is equal to z_(im) before being used in the calculation.

Returning to the fitting step E7-1, the latter comprises a step E7-1-2 of calculating the atomic number correction term φ _(i) for the said corresponding chemical element. In particular, this calculation step uses the two incidence correction terms Θ and Θ _(im) described hereinabove calculated in the course of the said cycle, these calculated terms being those belonging to the said step cycle in progress, stated otherwise step E7-1-2 is carried out after step E7-1-1.

According to a particular implementation, each step of calculating the atomic number correction term φ _(i) uses the following relation:

$\begin{matrix} {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{\theta}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{\theta}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{\theta}} \right)^{n}}} \right)}}}} & \left( {{eq}.\mspace{14mu} 9} \right) \end{matrix}$

with I_(igco) the intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the said electron beam 1, ξ_(i) the zeta-factor associated with the said corresponding chemical element, n a parameter depending on the mean atomic number Zc of the object at the level of the said zone Z1, α a parameter depending on the mean atomic number Zc of the object at the level of the said zone Z1, β_(i) a term making it possible to fit the maximum of the term φ _(i) and z_(θ) the thickness in the direction of incidence determined on the basis of the incidence correction terms Θ and Θ _(im), calculated in the course of the said cycle (during steps E7-0 and E7-1-1 which are implemented before this step E7-1-2), especially in the manner as indicated hereinabove by using equations (eq. 4) to (eq. 8) hereinabove.

In particular, the parameter n is determined by the following relation:

n=n ₁ Ln

_(c) +n ₂  (eq. 10)

with the parameters n₁ and n₂ given by a chart giving the value of n as a function of

_(c) whatever the power of the electron beam. FIG. 6 specifically shows the variation of the parameter n as a function of the mean atomic number

_(c) for various known powers of the electron beam. In particular, it has been able to be deduced from this FIG. 6 that n₁ was preferentially equal to −0.266 and n₂ was preferentially equal to 2.222 in this sense, the application of the Napierian logarithm to the corresponding value of the mean atomic number can be sufficient to solve equation (eq. 10).

It was specified hereinabove that the parameter α was dependent on the mean atomic number

_(c), in particular the parameter α is determined by the following relation:

$\begin{matrix} {\alpha = ^{({{\alpha_{1}{({L\; n\; _{c}})}}^{2} + {\alpha_{2}L\; n\; _{c}} + \alpha_{3}})}} & \left( {{eq}.\mspace{14mu} 11} \right) \end{matrix}$

with α₁, α₂ and α₃ parameters depending on the initial energy E₀ of the electrons of the electron beam. FIG. 7 illustrates the variation of the parameter α as a function of the mean atomic number

_(c) for various known powers of the electron beam (here 10 kV, 20 kV and 30 kV).

It is understood that the parameters n and α have been defined empirically by fitting the term φ _(i) calculated with equation (eq. 9) to the values deduced from the simulations for the set of pure chemical elements and objects studied. For example, the simulation of the atomic number correction term φ _(i) for various compositions and thicknesses of wafer at 30 kV is illustrated in FIG. 8. In this FIG. 8, the data points are calculated using the intensities of the X-ray radiation generated by Monte-Carlo simulation and the dashed curves are calculated and fitted to the data points by optimizing the parameters n and α.

The term β_(i) is determined by supposing that, for any thickness greater than or equal to a maximum ionization depth z_(im) of the corresponding chemical element, the intensity of the X-ray radiation generated in the object 2 is equivalent to that of the object 2 if the latter is opaque to the said electron beam. The term β_(i) is then given by the following equation:

$\begin{matrix} {\beta_{i} = \left\{ \begin{matrix} {{\left( {\rho \; z_{im}} \right)^{n}\frac{\left( {{\frac{\xi_{i}}{C_{ic}}\frac{I_{igco}}{\rho \; z_{im}}} - 1} \right)}{{\alpha \left( {\rho \; z_{im}} \right)}^{n} - \left( {{\frac{\xi_{i}}{C_{ic}}\frac{I_{igco}}{\rho \; z_{im}}} - 1} \right)}},} & {{{if}\mspace{14mu} \beta_{i}} > 0} \\ {0,} & {{{if}\mspace{14mu} \beta_{i}} \leq 0} \end{matrix} \right.} & \left( {{eq}.\mspace{14mu} 12} \right) \end{matrix}$

The parameters used in the calculation of β_(i) being those defined previously and especially in the course of the said cycle of steps in progress.

The term although advantageous, can be neglected (β_(i)=0) when the thickness z₀ of the object 2 is at least twice as small as a thickness z _(i) (defined hereinafter) for which the atomic number correction term φ _(i) is a maximum.

The thickness z _(i) is then calculated by solving the following equation, especially by iterative calculation:

$\begin{matrix} {\left( {\rho {\overset{\_}{z}}_{i}} \right)^{1 + n} = \frac{\begin{matrix} {{n\; \xi_{i}{I_{igco}\left( {1 + {\beta_{i}/\left( {\rho \; {\overset{\_}{z}}_{i}} \right)^{n}}} \right)}^{2}} -} \\ {\rho \; {{\overset{\_}{z}}_{i}\left\lbrack {1 + n + {\left( {1 + {2n}} \right){\beta_{i}/\left( {\rho \; {\overset{\_}{z}}_{i}} \right)^{n}}}} \right\rbrack}} \end{matrix}}{\alpha \left\lbrack {1 + {\left( {1 + n} \right){\beta_{i}/\left( {\rho {\overset{\_}{z}}_{i}} \right)^{n}}}} \right\rbrack}} & \left( {{eq}.\mspace{14mu} 13} \right) \end{matrix}$

With n, α and β_(i) defined by relations (eq. 10), (eq. 11) and (eq. 12) respectively.

According to a particular embodiment, the term z _(i) can be calculated through the following equation:

$\begin{matrix} {{\overset{\_}{Z}}_{i} = {{\overset{\_}{Z}}_{ip}\frac{\rho_{i}}{\rho}{\frac{n}{n_{i}}\left\lbrack {1 + {0.048\mspace{11mu} \left( {2.5 - \frac{E_{0}}{20}} \right)\left( {1 - {LnM}_{i} + \frac{\left( {LnM}_{i} \right)^{2}}{3}} \right)\left( {\frac{M_{c}}{M_{i}} - 1} \right)}} \right\rbrack}}} & \left( {{eq}.\mspace{14mu} 14} \right) \end{matrix}$

with z _(ip) the thickness for which the atomic number correction term φ _(i) for the corresponding pure chemical element is a maximum, n and n_(i) the parameters depending respectively on the mean atomic number of the object and on the atomic number of the corresponding pure element in particular as defined in equation (eq. 10) hereinabove (n_(i) can be calculated with equation 10 by replacing Zc by Zi of the pure chemical element), ρ and ρ_(i) the densities respectively of the object and of the corresponding pure chemical element and M_(c) and M_(i) the atomic masses of the object and of the corresponding pure chemical element.

Although equation 14 gives an approximate value, it will be preferred to equation 13 which gives the exact result, since it is less greedy in terms of calculational resources.

The thickness z _(ip) of the corresponding pure chemical element is calculated by solving equation 13. This can be done upstream just once for each chemical element so that the method uses a reading of z _(ip) in a table whose input is the chemical element identified.

Concerning the thickness z_(θ) which corresponds to the thickness traversed by the electron beam in the direction of incidence θ, it can be deduced on the basis of the two incidence correction terms Θ and Θ _(im), by supposing in particular the following equations:

$\begin{matrix} {z_{\theta} = {{Min}\left( {\frac{z_{0}}{\overset{\_}{\Theta}\cos \; \theta},Z_{i\; \theta}} \right)}} & \left( {{eq}.\mspace{14mu} 15} \right) \\ {z_{i\; \theta} = \frac{z_{im}}{{\overset{\_}{\Theta}}_{im}\cos \; \theta}} & \left( {{eq}.\mspace{14mu} 16} \right) \end{matrix}$

With z_(θ) the thickness in the direction of incidence θ taking into account the angle of incidence θ and z_(iθ) the maximum thickness of ionization of the corresponding chemical element according to the direction of incidence θ.

Furthermore, the fitting step E7-1 comprises a step E7-1-3 of calculating an absorption correction term χ _(i) for the said corresponding chemical element. The purpose of this absorption correction term χ _(i) is to take into account the absorption by the object of the X-ray radiation generated by the corresponding chemical element. Stated otherwise, the absorption correction term χ _(i) makes it possible to correct the influence of the object on the X-ray radiation generated. In particular, the calculation of the absorption correction term χ _(i) for the said corresponding chemical element uses the incidence correction terms Θ and Θ _(im) calculated in the course of the said cycle, as well as the atomic number correction term φ _(i), calculated in the course of the said cycle (it is understood that step E7-1-3 is then implemented after step E7-1-1, step E7-1-2 and step E7-0).

According to a particular embodiment, each step of calculating the absorption correction term χ _(i) makes use of solving the equation

$\begin{matrix} {{\overset{\_}{\chi}}_{i} = \left\{ \begin{matrix} {\frac{\chi_{ic}\rho \; z_{0}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}}{\begin{matrix} {{\phi_{i}(0)} + \frac{P_{i}}{\chi_{ic}} +} \\ \begin{Bmatrix} {{P_{i}^{\prime}\left( {\frac{1}{\chi_{ic}} - {\rho \; z_{0}}} \right)} - \left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}}{\chi_{ic}}} \right\rbrack +} \\ {\left( {P_{i}^{\prime} - P_{i}} \right)\rho \; z_{ib}} \end{Bmatrix} \\ {^{{- \chi_{ic}}{\rho z}_{ib}} - {\left\lbrack {{\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}^{\prime}}{\chi_{ic}}} \right\rbrack ^{{- \chi_{ic}}\rho \; z_{0}}}} \end{matrix}},} & {{{if}\mspace{14mu} z_{ib}} > 0} \\ {\frac{\rho \; z_{0}\chi_{ic}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}}{{\phi_{i}(0)} + \frac{P_{i}^{''}}{\chi_{ic}} - {\left\{ {{P_{i}^{''}\left( {\frac{1}{\chi_{ic}} + {\rho \; z_{0}}} \right)} + {\phi_{i}(0)}} \right\} ^{{- \chi_{ic}}\rho \; z_{0}}}},} & {{{if}\mspace{14mu} z_{ib}} \leq 0} \end{matrix} \right.} & \left( {{eq}.\mspace{14mu} 17} \right) \end{matrix}$

With φ _(i)(0) the value of the distribution φ _(i)(ρz) of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element, with z in φ _(i)(ρz) varying from 0 to z₀, φ _(i)(ρz₀) the value of the distribution φ _(i)(ρz) of the intensities of the X-ray radiation generated at the depth z₀ of the object by the corresponding chemical element (also called the term for the ionization at the depth z₀), P_(i) the initial slope of the distribution φ _(i)(ρz) of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element and determined in the following manner:

$\begin{matrix} {P_{i} = {\frac{g.h^{4}.\mspace{14mu} \left( {F/\overset{\_}{R}} \right)^{2}}{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{i\; \theta}} \right)}\rho \; z_{i\; \theta}}\frac{1}{\left( {\cos \; \theta} \right)^{4}}}} & \left( {{eq}\mspace{14mu} 18} \right) \end{matrix}$

With φ _(i)(ρz_(iθ)) calculated with eq. 9 by replacing z_(θ) with z_(iθ), z_(iθ) determined by equation 16 and g, h and (F/R) parameters known to the person skilled in the art, in particular determined according to the publication of Pouchou J. L. and Pichoir F. (1991) on page 40 “Quantitative analysis of homogeneous or stratified microvolumes applying the model PAP, Electron Probe Quantitation, In: Heinrich & Newbury (Eds) Plenum Press, New York, p. 31”

In particular, employing the terms of the present description, we have:

$\begin{matrix} {\mspace{79mu} {g = {0.22\left( {1 - {2^{{- \frac{_{c}}{15}}{({\frac{E_{0}}{E_{is}} - 1})}}}} \right)\; {\ln \left( {4_{C}} \right)}}}} & \left( {{{eq}.\mspace{14mu} 18}a} \right) \\ {\mspace{79mu} {h = {1 - {10\frac{1 - \frac{1}{1 + \frac{E_{0}}{10\; E_{is}}}}{_{C}^{2}}}}}} & \left( {{{eq}.\mspace{14mu} 18}b} \right) \\ {{F/\overset{\_}{R}} = {1 + \frac{\left\lbrack {1 + {1.3\mspace{11mu} {\ln \left( _{C} \right)}}} \right\rbrack \; {\ln \left\lbrack {1 + {\left( {0.2 + \frac{_{C}}{200}} \right)\left( {1 - \left\{ \frac{E_{is}}{E_{0}} \right\}^{0.42}} \right)}} \right\rbrack}}{\ln \left( {1 + 0.2 + \frac{_{C}}{200}} \right)}}} & \left( {{{eq}.\mspace{14mu} 18}c} \right) \end{matrix}$

χ_(ic) is the mass absorption coefficient of the compound for the characteristic X-ray radiation of the corresponding chemical element:

χ_(ic)=cosec(ψ+θ)Σ_(i+1) ^(N) C _(ic)(μ/ρ)_(i) ^(ip)  (eq 19)

With the angle of elevation of the X-ray detector with respect to the normal, θ the angle of incidence of the electron beam, C_(ic) the concentration of the chemical element and (μ/ρ)_(i) ^(ip) the mass absorption coefficient of the pure chemical element.

Furthermore, φ _(i)(ρz_(θ)) is the atomic number correction term defined by eq.9 and calculated in the course of the said cycle.

Still within the framework of equation 17, we have:

$\begin{matrix} {{P_{i}^{\prime} = \frac{\left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack^{2} + {2P_{i}\rho \; {z_{0}\left\lbrack {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack}}}{\rho \; {z_{0}\left\lbrack {{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}} - {2{\phi_{i}(0)}} - {P_{i}\rho \; z_{0}}} \right\rbrack}}},} & \left( {{eq}.\mspace{14mu} 20} \right) \\ {{P_{i}^{''} = {2\frac{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} - {\phi_{i}(0)}}{\rho \; z_{0}}}},{and}} & \left( {{eq}.\mspace{14mu} 21} \right) \\ {z_{ib} = {z_{0}{\frac{{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}} - {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}{{P_{i}\rho \; z_{0}} + {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}.}}} & \left( {{eq}.\mspace{14mu} 22} \right) \end{matrix}$

In particular, z_(θ) is obtained according to equations 15 and 16 which depend on the incidence correction terms calculated in the course of the said cycle.

Within the framework of equation eq. 17 making it possible to calculate the absorption correction term χ _(i), the parameter φ_(i)(0) can be calculated in the following manner:

$\begin{matrix} {{\phi_{i}(0)} = \left\{ \begin{matrix} {{1 + {\left\lbrack {{\phi_{im}(0)} - 1} \right\rbrack \frac{z_{0}}{{\overset{\_}{z}}_{i}}}},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i}} \\ {{\phi_{im}(0)},} & {{{if}\mspace{14mu} z_{0}} \geq {\overset{\_}{z}}_{i}} \end{matrix} \right.} & \left( {{eq}.\mspace{14mu} 23} \right) \end{matrix}$

with z _(i) as defined by equations eq. 13 or 14 and φ_(im)(0) the surface ionization of the corresponding chemical element in the object considered to be opaque to the said electron beam and determined in a manner known to the person skilled in the art, in particular determined according to the publication of Pouchou J. L. and Pichoir F. (1991) Quantitative analysis of homogeneous or stratified microvolumes applying the model PAP, Electron Probe Quantitation, In: Heinrich & Newbury (Eds) Plenum Press, New York, p. 31 in the guise of surface ionization term.

According to a particular implementation of the step of calculating the absorption correction term making it possible to optimize the calculated value, the calculation step comprises a step of determining a parameter z _(iθ) corresponding to the minimum value between z _(i) defined by equations eq. 13 or eq. 14 and z_(iθ) defined by equation eq. 16 and defined by the relation:

z _(iθ)=Min( z _(i) ,z _(iθ))  (eq 24)

The term φ _(i)(ρz₀) is determined in the following manner:

$\begin{matrix} {{\phi_{i}\left( {\rho \; z_{0}} \right)} = \left\{ \begin{matrix} {{\left\{ {{\left\lbrack {\frac{3}{2} - {\phi_{i}(0)}} \right\rbrack {\frac{z_{0}}{{\overset{\_}{z}}_{i\; \theta}}\left\lbrack {2 - \frac{z_{0}}{{\overset{\_}{z}}_{i\; \theta}}} \right\rbrack}} + {\phi_{i}(0)}} \right\} \cos \; \theta},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i\; \theta}} \\ {{\frac{3}{2}\left\{ {{\left\lbrack \frac{z_{0} - {\overset{\_}{z}}_{i\; \theta}}{z_{i\; m} - {\overset{\_}{z}}_{i\; \theta}} \right\rbrack \left\lbrack {\frac{z_{0} - {\overset{\_}{z}}_{i\; \theta}}{z_{i\; m} - {\overset{\_}{z}}_{i\; \theta}} - 2} \right\rbrack} + 1} \right\} \cos \; \theta},} & {{{if}\mspace{14mu} z_{i\; \theta}} \leq z_{0} \leq z_{im}} \\ 0 & {{{if}\mspace{14mu} z_{0}} > z_{im}} \end{matrix} \right.} & \left( {{eq}.\mspace{14mu} 25} \right) \end{matrix}$

with φ _(i)(0) calculated according to equation (eq. 23).

According to an alternative, it is possible to simplify the calculations of the atomic number correction and absorption correction terms in the particular case of a wafer perpendicular to the axis of the beam. In this case, the angle of incidence θ is zero, the consequence of this being that the two incidence correction terms Θ and Θ _(im) are equal to 1 so that the atomic number correction term φ _(i) is determined according to the following equation:

$\begin{matrix} {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{0}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{0}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{0}} \right)^{n}}} \right)}}}} & \left( {{eq}.\mspace{14mu} 26} \right) \end{matrix}$

The parameters of φ _(i)(ρz₀) within the framework of this alternative are such as already described. Still within the framework of this alternative, the absorption correction term can be calculated by solving equation (eq. 17) with the use of equations (eq. 20), (eq. 21), (eq.22), by replacing in these equations φ _(i)(ρz_(θ)) by φ _(i)(ρz₀), with P_(i) the initial slope of the distribution φ _(i)(ρz)—z varying here from 0 to z₀—of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element and determined in the following manner:

$\begin{matrix} {P_{i} = \frac{g.h^{4}.\left( {F/\overset{\_}{R}} \right)^{2}}{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{im}} \right)}\rho \; z_{im}}} & \left( {{eq}\mspace{14mu} 27} \right) \end{matrix}$

With φ _(i)(ρz_(im)) calculated with eq 26 by replacing z₀ with z_(im), z_(im) determined by equation 6 and g, h and (F/R) known parameters, in particular determined according to the publication of Pouchou J. L. and Pichoir F. (1991) Quantitative analysis of homogeneous or stratified microvolumes applying the model PAP, Electron Probe Quantitation, In: Heinrich & Newbury (Eds) Plenum Press, New York, p. 31

χ_(ic) the mass absorption coefficient of the characteristic X-ray radiation of the corresponding chemical element:

χ_(ic)=cosec(ψ)Σ_(i=1) ^(N) C _(ic)(μ/ρ)_(i) ^(ip)  eq 28

Within the framework of the zero angle of incidence; the term φ _(i)(ρz₀) is determined in the following manner:

$\begin{matrix} {{\phi_{i}\left( {\rho \; z_{0}} \right)} = \left\{ {\begin{matrix} {{{\left\lbrack {\frac{3}{2} - {\phi_{i}(0)}} \right\rbrack {\frac{z_{0}}{{\overset{\_}{z}}_{i}}\left\lbrack {2 - \frac{z_{0}}{{\overset{\_}{z}}_{i}}} \right\rbrack}} + {\phi_{i}(0)}},} & {{{if}{\mspace{14mu} \;}z_{0}} < {\overset{\_}{z}}_{i}} \\ {{\frac{3}{2}\left\{ {{\left\lbrack \frac{z_{0} - {\overset{\_}{z}}_{i}}{z_{im} - {\overset{\_}{z}}_{i}} \right\rbrack \left\lbrack {\frac{z_{0} - {\overset{\_}{z}}_{i}}{z_{im} - {\overset{\_}{z}}_{i}} - 2} \right\rbrack} + 1} \right\}},} & {{{if}\mspace{14mu} {\overset{\_}{z}}_{i}} \leq z_{0} \leq z_{im}} \\ 0 & {{{if}\mspace{14mu} z_{0}} > z_{im}} \end{matrix},} \right.} & \left( {{eq}.\mspace{14mu} 29} \right) \end{matrix}$

φ_(i)(0) defined by eq.23, z _(i) defined according to equations 13 or 14.

Various ways of calculating the atomic number correction and absorption correction terms were seen previously.

Once these terms have been calculated, the said cycle of steps E7 comprises a step E7-2 of modifying the intermediate value of mass-thickness ρz₀ using the incidence correction term Θ calculated in the course of the said cycle, and the incidence correction Θ _(im), atomic number correction φ _(i) and absorption correction χ _(i) terms calculated in the course of the said cycle for each chemical element and dependent on each measurement step E3.

In particular, the intermediate value of mass-thickness can be determined according to the following formulation:

$\begin{matrix} {{{\rho \; z_{0}} = {\overset{\_}{\Theta}\mspace{14mu} \cos \; \theta \; {\sum_{i = 1}^{N}{\xi_{i}\frac{I_{igc}}{{\overset{\_}{\phi}}_{i}}}}}}\;} & \left( {{eq}.\mspace{14mu} 30} \right) \end{matrix}$

With the application of the following formulation for the intensity of the X-ray radiation generated by the chemical element i in the object I_(igc):

I _(igc)=χ _(i) I _(iec)  (eq. 31)

In these formulae, it is clearly understood that for each cycle E7 it is the values calculated in the course of the said cycle E7 of the incidence correction, atomic number correction and absorption correction terms which are used to modify in the course of the same cycle the intermediate values of mass-thickness and of concentration.

Furthermore, the said cycle of steps E7 comprises a step E7-3 of modifying, for each chemical element, the intermediate value of concentration C_(ic) of the said corresponding chemical element using the intermediate value of mass-thickness ρz₀ as modified in the course of the said cycle, the incidence correction term Θ, calculated in the course of the said cycle, and the incidence correction Θ _(im), atomic number correction φ _(i) and absorption correction χ _(i) terms calculated in the course of the said cycle and corresponding to the said chemical element.

Stated otherwise, in the course of each cycle E7 the intermediate value of the mass-thickness is modified (step E7-2) according to the following formula

$\begin{matrix} {{{\rho \; z_{0}} = {\overset{\_}{\Theta}\mspace{14mu} \cos \; \theta \; {\sum_{i = 1}^{N}{\xi_{i}\frac{{\overset{\_}{\chi}}_{i}I_{iec}}{{\overset{\_}{\phi}}_{i}}}}}}\;} & \left( {{eq}.\mspace{14mu} 32} \right) \end{matrix}$

with N the total number of chemical elements identified, i the index of the current chemical element studied, I_(iec) the intensity of the emergent X-ray radiation corresponding to the said chemical element of index i, χ _(i) the absorption correction term calculated in the course of the said cycle and corresponding to the said chemical element of index i, ξ_(i) the zeta-factor associated with the said chemical element of index i, the atomic number correction term φ _(i) calculated in the course of the said cycle and corresponding to the said chemical element of index i, Θ the incidence correction term calculated in the course of the said cycle.

In particular, for each chemical element, the intermediate value of concentration C_(ic), can be calculated (step E7-3) using the following formula:

$\begin{matrix} {C_{ic} = {\frac{\xi_{i}}{\rho \; z_{0}}\frac{I_{igc}}{{\overset{\_}{\phi}}_{i}}\overset{\_}{\Theta}\; \cos \; \theta}} & \left( {{eq}.\mspace{14mu} 33} \right) \end{matrix}$

In which I_(igc) is determined according to equation (eq. 31), ρz₀ corresponds to the mass-thickness value as modified in the course of the said corresponding cycle of steps, Θ corresponding to the incidence correction term calculated in the course of the said cycle and φ _(i) corresponding to the atomic number correction term as calculated in the course of the said corresponding cycle of steps. Stated otherwise, in the course of each cycle the intermediate value of concentration C_(ic) of each chemical element is calculated according to the following formula:

$\begin{matrix} {C_{ic} = {\frac{\xi_{i}}{\rho \; z_{0}}\frac{{\overset{\_}{\chi}}_{i}I_{iec}}{{\overset{\_}{\phi}}_{i}}\overset{\_}{\Theta}\; \cos \; \theta}} & \left( {{eq}.\mspace{14mu} 34} \right) \end{matrix}$

with I_(iec) the measured intensity of the emergent X-ray radiation of the said corresponding chemical element, ρz₀ the intermediate mass-thickness value modified in the course of the said cycle, χ _(i) the absorption correction term for the said corresponding chemical element calculated in the course of the said cycle, ξ_(i) the zeta-factor associated with the said corresponding chemical element, Θ the incidence correction term calculated in the course of the said cycle, the atomic number correction term φ _(i) calculated in the course of the said cycle for the said corresponding chemical element.

The iteration of the step E7 cycle is halted when the variation, between two successive iterations of the intermediate values of mass-thickness ρz₀ and of the intermediate values of concentration C_(ic) of each chemical element, is less than an associated predetermined threshold, the said modified intermediate mass-thickness value defining the mass-thickness value determined and each modified intermediate concentration value defining the corresponding concentration value determined.

The method described hereinabove makes it possible to study a precise zone of the object. According to need, it may be useful to analyse the object in its entirety. In this sense, the invention also relates to a method for studying an object comprising the following steps:

-   -   Dividing the object into several zones to be studied,     -   Implementing, for each zone, the said method of study as         described previously with a view to determining the         corresponding mass-thickness value and, for each chemical         element of the said zone, the corresponding concentration value.

The methods described hereinabove make it possible in particular to calculate the thickness and the composition of a semi-transparent/semi-opaque thin wafer on the basis of a measurement by EDS (energy dispersive spectrometry) in an SEM (scanning electron microscope), it not being possible to do this using any current scheme, namely neither the k-factor scheme, nor the φρz scheme. Moreover, the invention combines both precision and speed of the calculations making it possible to produce, in real time, reliable profiles and maps, to better than 5% in most cases, of the distribution of the mass-thicknesses and concentrations.

In a general manner, the methods described hereinabove are potentially of interest to all EDS system constructors for SEM in so far as it allows the simultaneous analysis of the composition and the mass-thickness of any homogeneous type of materials, whatever its thickness and its composition. At least two types of materials are concerned:

-   -   thin wafers prepared by FIB for “Focused Ion Beam” (thicknesses         varying between 100 and 300 nm) or by any other polishing         technique (ultra-microtomy, mechanical, chemical or ion         polishing),     -   any type of materials deposited on a transparent TEM         (“Transmission Electron Microscope”) grid (nanowires,         nanoparticles, etc.).

Another application relates to the characterization of reference thin wafers for EDS quantitative analysis in transmission electron microscopy (TEM). Indeed, quantitative analysis by TEM/EDS requires calibration of the spectrometer by means of reference thin wafers whose composition and thickness must be determined beforehand. 

1. Method for studying a zone of an object, the zone exhibiting a mass-thickness and comprising at least one chemical element, wherein the method comprises: a step of exposing a part of the zone of the object to an electron beam, a step of identifying each chemical element present in the zone by virtue of the exposure step, a step of measuring, for each chemical element identified, a corresponding intensity of an X-ray radiation emergent from the object on account of the exposure step, a step of determining a value of the mass-thickness dependent on each measurement step, a step of determining a value of the concentration of each chemical element identified using the value of the mass-thickness determined, wherein the method comprises an initialization step in which an intermediate value of the mass-thickness ρz₀, with ρ an assumed density and z₀ an assumed thickness of the object at the level of the zone, and an intermediate value of concentration C_(ic) of each chemical element identified are determined by choice, and wherein the method comprises an iterative cycle of steps comprising for each iteration of the said cycle: a step of calculating an incidence correction term Θ intended to take account of an angle of incidence θ of the electron beam and associated with the zone studied, a fitting step, implemented for each chemical element identified, and comprising: a step of calculating an incidence correction term Θ _(im) associated with the chemical element identified and intended to take account of the angle of incidence θ of the electron beam, a step of calculating an atomic number correction term φ _(i) for the corresponding chemical element using the incidence correction terms Θ and Θ _(im) calculated in the course of the said cycle, a step of calculating an absorption correction term χ _(i) for the corresponding chemical element using the incidence correction terms Θ and Θ _(im) calculated in the course of the said cycle and the atomic number correction term φ _(i) calculated in the course of the said cycle, a step of modifying the intermediate value of mass-thickness ρz₀ using the incidence correction term Θ calculated in the course of the cycle and the incidence correction Θ _(im), atomic number correction φ _(i) and absorption correction χ _(i) terms calculated in the course of the cycle for each chemical element and dependent on each measurement step, a step of modifying, for each chemical element, the intermediate value of concentration C_(ic) of the corresponding chemical element using the intermediate value of mass-thickness ρz₀ as modified in the course of the cycle, the incidence correction term Θ, calculated in the course of the cycle, and the incidence correction Θ _(im), atomic number correction φ _(i) and absorption correction χ _(i) terms calculated in the course of the cycle and corresponding to the chemical element, wherein the iteration is halted when a variation, between two successive iterations of the intermediate values of mass-thickness ρz₀ and of the intermediate values of concentration C_(ic) of each chemical element, is less than an associated predetermined threshold, the modified intermediate mass-thickness value defining the mass-thickness value determined and each modified intermediate concentration value defining the corresponding concentration value determined.
 2. Method according to claim 1, wherein each step of calculating the incidence correction term Θ comprises solving the following equation: $\overset{\_}{\Theta} = \left\{ {1 + \left\lbrack {\frac{\rho \; z_{0}}{\cos \; \theta}{f\left( {Z -_{c}} \right)}{- 2}\frac{\cos \; \theta}{\rho}{\left( {1 - {\left. \quad ^{14{({1 - \rho})}\frac{\rho \; z_{0}}{\cos \; \theta}{f({Z -_{c}})}} \right)^{{- 2}\frac{\rho \; z_{0}}{\cos \; \theta}{f({Z -_{c}})}}}} \right\rbrack\left\lbrack {\frac{1}{\cos \; \theta} - 1} \right\rbrack}} \right\}^{0.6}} \right.$ and wherein each step of calculating the incidence correction term Θ _(im) comprises solving the following equation: ${\overset{\_}{\Theta}}_{im} = \left\{ {1 + {\left\lbrack {{\frac{\rho \; z_{im}}{\cos \; \theta}{f_{m}\left( E_{is} \right)}} - {2\frac{\cos \; \theta}{\rho}^{{- 2}\frac{\rho \; z_{im}}{\cos \; \theta}{f_{m}{(E_{is})}}}}} \right\rbrack \left\lbrack {\frac{1}{\cos \; \theta} - 1} \right\rbrack}} \right\}^{0.6}$ with

_(c) a mean atomic number of the object at the level of the zone, ƒ(

_(c)) a function of the mean atomic number

_(c), z_(im) a maximum ionization depth of the corresponding chemical element, ƒ_(m)(E_(is)) a function of an ionization threshold energy E_(is) of the energy level considered of a corresponding chemical element.
 3. Method according to claim 2, wherein f(Z−_(c)) = ^(a(LnZ−_(c))⁴ + b(LnZ−_(c))³ + c(LnZ−_(c))² + dLn Z−_(c)+e ) with a, b, c, d, e parameters being determined by Monte-Carlo simulation and depending on an energy of electrons of the electron beam.
 4. Method according to claim 2, wherein ${{f_{m}\left( E_{is} \right)} = \frac{{AE}_{is}^{m}}{\left( {R_{p}/S_{p}} \right)_{i}}},$ with (R_(p)/S_(p))_(i) being the ratio of backscattering coefficients R_(p) and of a stopping power S_(p) for the corresponding pure chemical element, and A and m being parameters determined by Monte-Carlo simulation and depending on the energy level for the corresponding chemical element.
 5. Method according to claim 1, wherein each step of calculating the atomic number correction term φ _(i) uses the following relation ${{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{\theta}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{\theta}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{\theta}} \right)^{n}}} \right)}}}},$ with I_(igco) an intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the electron beam, ξ_(i) a zeta-factor associated with the corresponding chemical element, n a parameter depending on a mean atomic number Zc of the object at the level of the zone, α a parameter depending on the mean atomic number Zc of the object at the level of the zone, β_(i) a term making it possible to fit a maximum of the term φ _(i) and z_(θ) a thickness in the direction of incidence θ determined on the basis of the incidence correction terms Θ and Θ _(im) calculated in the course of the cycle.
 6. Method according to claim 5, wherein the parameter n is determined by the following relation n=n₁ Ln

_(c)+n₂, the parameters n₁ and n₂ being given by a chart giving a value of n as a function of

_(c) whatever a power of the electron beam.
 7. Method according to claim 5, wherein the parameter α is determined by the following relation  = ^((α₁(LnZ−_(c))² + α₂LnZ−_(c)+α₃)), with α₁, α₂ and α₃ parameters depending on an initial energy E₀ of electrons of the electron beam.
 8. Method according to claim 5, wherein the term β_(i) is determined by supposing that, for any thickness greater than or equal to a maximum ionization depth z_(im) of the corresponding chemical element, the intensity of the X-ray radiation generated in the object is equivalent to that of the object if the object is opaque to the electron beam.
 9. Method according to claim 8, wherein the term β_(i) is obtained by solving the following equation: $\beta_{i} = \left\{ {\begin{matrix} {{\left( {\rho \; z_{im}} \right)^{n}\frac{\left( {{\frac{\xi_{i}}{C_{ic}}\frac{I_{igco}}{\rho \; z_{im}}} - 1} \right)}{{\alpha \left( {\rho \; z_{im}} \right)}^{n} - \left( {{\frac{\xi_{i}}{C_{ic}}\frac{I_{igco}}{\rho \; z_{im}}} - 1} \right)}},} & {{{{if}\mspace{20mu} \beta_{i}} > 0}\;} \\ {0,} & {{{if}\mspace{20mu} \beta_{i\;}} \leq 0} \end{matrix},} \right.$ with z_(im) being a maximum ionization depth of the corresponding chemical element.
 10. Method according to claim 1, wherein each step of calculating the absorption correction term χ _(i) makes use of solving the equation ${\overset{\_}{\chi}}_{i} = {{\quad\quad}\left\{ \begin{matrix} {\frac{\chi_{ic}\rho \; z_{0}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}}{\begin{matrix} {{\phi_{i}(0)} + \frac{P_{i}}{\chi_{ic}} + \begin{Bmatrix} {{P_{i}^{\prime}\left( {\frac{1}{\chi_{ic}} - {\rho \; z_{0}}} \right)} - \left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}}{\chi_{ic}}} \right\rbrack +} \\ {\left( {P_{i}^{\prime} - P_{i}} \right)\rho \; z_{ib}} \end{Bmatrix}} \\ {e^{{- \chi_{ic}}\rho \; z_{ib}} - {\left\lbrack {{\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}^{\;^{\prime}}}{\chi_{ic}}} \right\rbrack e^{{- \chi_{ic}}\rho \; z_{0}}}} \end{matrix}},} & {{{if}\mspace{14mu} z_{ib}} > 0} \\ {\frac{\rho \; z_{0}\chi_{ic}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}}{{\phi_{i}(0)} + {\frac{P_{i}^{''}}{\chi_{ic}}\left\{ {{P_{i}^{''}\left( {\frac{1}{\chi_{ic}} + {\rho \; z_{0}}} \right)} + {\phi_{i}(0)}} \right\} e^{- \chi_{{ic}^{\rho \; z_{0}}}}}},} & {{{if}\mspace{14mu} z_{ib}} \leq 0} \end{matrix} \right.}$ with φ_(i)(0) being a value of a distribution of intensities of the X-ray radiation generated at a surface of the object by the corresponding chemical element, φ_(i)(ρz₀) a value of the distribution of the intensities of the X-ray radiation generated at the depth z₀ of the object by the corresponding chemical element, P_(i) an initial slope of the distribution of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element and determined by the relation ${P_{i} = {\frac{g \cdot h^{4} \cdot \left( {F/\overset{\_}{R}} \right)^{2}}{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{i\; \theta}} \right)}\rho \; z_{i\; \theta}}\frac{1}{\left( {\cos \theta} \right)^{4}}\mspace{14mu} {with}}}{\mspace{11mu} \;}$ ${{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{i\; \theta}} \right)} = {{\frac{1 + {\alpha \left( {\rho \; z_{i\; \theta}} \right)}^{n}}{1 + {\frac{{\alpha C}_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{i\; \theta}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{i\; \theta}} \right)^{n}}} \right)}}}\mspace{14mu} {and}\mspace{14mu} z_{i\; \theta}} = \frac{z_{im}}{{\overset{\_}{\Theta}}_{im}{\cos \theta}}}},}\;$ χ_(ic) representing a mass absorption coefficient of a compound for the characteristic X-ray radiation of the corresponding chemical element, φ _(i)(ρz_(θ)) being the atomic number correction term calculated in the course of the cycle, ${P_{i}^{\prime} = \frac{\left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack^{2} + {2P_{i}\rho \; {z_{0}\left\lbrack {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack}}}{\rho \; {z_{0}\left\lbrack {{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}} - {2{\phi_{i}(0)}} - {P_{i}\rho \; z_{0}}} \right\rbrack}}},{P_{i}^{''} = {2\frac{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} - {\phi_{i}(0)}}{\rho \; z_{0}}}},{z_{ib} = {z_{0}\frac{{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)}} - {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}{{P_{i}\rho \; z_{0}} + {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}}},$ z_(im) a maximum ionization depth of the corresponding chemical element, β_(i) a term making it possible to fit a maximum of the atomic number correction term, I_(igco) an intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the electron beam, ξ_(i) a zeta-factor associated with the corresponding chemical element, α a parameter depending on the mean atomic number Zc of the object at the level of the said zone (Z1), n a parameter depending on the mean atomic number Zc of the object at the level of the zone and z_(θ) a depth of the object at the level of the said zone while taking account of the incidence θ of the electron beam.
 11. Method according to claim 10, wherein the parameter φ_(i) (0) is calculated in the following manner: $\mspace{20mu} {{\phi_{i}(0)} = \left\{ {{{\begin{matrix} {{1 + {\left\lbrack {{\phi_{im}(0)} - 1} \right\rbrack \frac{z_{0}}{\overset{\_}{{\overset{\_}{z}}_{i}}}}},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i}} \\ {{\phi_{im}(0)},} & {{{if}\mspace{14mu} z_{0}} \geq {\overset{\_}{z}}_{i}} \end{matrix}\mspace{14mu} {with}\mspace{11mu} \text{}{\overset{\_}{z}}_{i}} = {{\overset{\_}{z}}_{i_{p}}\frac{\rho_{i}}{\rho}{\frac{n}{n_{i}}\left\lbrack {1 + {0.048\left( {2.5 - \frac{E_{0}}{20}} \right)\left( {1 - {LnM}_{i} + \frac{\left( {LnM}_{i} \right)^{2}}{3}} \right)\left( {\frac{M_{c}}{M_{i}} - 1} \right)}} \right\rbrack}}},} \right.}$ φ_(im)(0) being a surface ionization of the corresponding chemical element in the object considered to be opaque to the said electron beam, z _(ip) a thickness for which the atomic number correction term φ _(i) for the corresponding pure chemical element is a maximum, n and n_(i) parameters depending respectively on the mean atomic number of the object and on the atomic number of the pure chemical element, ρ_(i) a density of the corresponding pure chemical element and M_(c) and M_(i) the atomic masses of the object and of the corresponding pure chemical element, and E₀ an initial energy of electrons of the electron beam.
 12. Method according to claim 11, comprising a step of determining a parameter z _(iθ) corresponding to the minimum value between z _(i) and z_(iθ) and defined by the following relation: z _(iθ)=Min(z _(i),z_(iθ)).
 13. Method according to claim 12, wherein the term φ_(i)(ρz₀) is determined in the following manner: ${\phi_{i}\left( {\rho \; z_{0}} \right)} = \left\{ {\begin{matrix} {{\left\{ {{\left\lbrack {\frac{3}{2} - {\phi_{i}(0)}} \right\rbrack {\frac{z_{0}}{{\overset{\_}{z}}_{i\; \theta}}\left\lbrack {2 - \frac{z_{0}}{{\overset{\_}{z}}_{i\; \theta}}} \right\rbrack}} + {\phi_{i}(0)}} \right\} {\cos \theta}},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i\; \theta}} \\ {{\frac{3}{2}\left\{ {{\left\lbrack \frac{z_{0} - {\overset{\_}{z}}_{i\; \theta}}{z_{im} - {\overset{\_}{z}}_{i\; \theta}} \right\rbrack \left\lbrack {\frac{z_{0} - {\overset{\_}{z}}_{i\; \theta}}{z_{im} - {\overset{\_}{z}}_{i\; \theta}} - 2} \right\rbrack} + 1} \right\} {\cos \theta}},} & {{{if}\mspace{14mu} {\overset{\_}{z}}_{i\; \theta}} \leq z_{0} \leq z_{im}} \\ 0 & {{{if}\mspace{14mu} z_{0}} > z_{im}} \end{matrix}.} \right.$
 14. Method according to claim 1, wherein the angle of incidence θ being zero then the two incidence correction terms Θ and Θ _(im) are equal to 1 so that the atomic number correction term is determined on the basis of the following equation ${{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{0}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{0}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{0}} \right)^{n}}} \right)}}}},$ with I_(igco) being an intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the said electron beam, ξ_(i) a zeta-factor associated with the corresponding chemical element, n a parameter depending on the mean atomic number Zc of the object at the level of the zone, α a parameter depending on the mean atomic number Zc of the object at the level of the zone, β_(i) a term making it possible to fit the maximum of the term φ _(i), and wherein ${\overset{\_}{\chi}}_{i} = {{\quad\quad}\left\{ {{\begin{matrix} {\frac{\chi_{ic}\rho \; z_{0}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}}{\begin{matrix} {{\phi_{i}(0)} + \frac{P_{i}}{\chi_{ic}} + \begin{Bmatrix} {{P_{i}^{\prime}\left( {\frac{1}{\chi_{ic}} - {\rho \; z_{0}}} \right)} -} \\ {\left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}}{\chi_{ic}}} \right\rbrack + {\left( {P_{i}^{\prime} - P_{i}} \right)\rho \; z_{ib}}} \end{Bmatrix}} \\ {e^{- \chi_{{ic}^{\rho \; z}{ib}}} - {\left\lbrack {{\phi_{i}\left( {\rho \; z_{0}} \right)} + \frac{P_{i}^{\prime}}{\chi_{ic}}} \right\rbrack e^{- \chi_{{ic}^{\rho \; z_{0}}}}}} \end{matrix}},} & {{{if}\mspace{14mu} z_{ib}} > 0} \\ {\frac{\rho \; z_{0}\chi_{ic}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}}{{\phi_{i}(0)} + {\frac{P_{i}^{''}}{\chi_{ic}}\left\{ {{P_{i}^{''}\left( {\frac{1}{\chi_{ic}} + {\rho \; z_{0}}} \right)} + {\phi_{i}(0)}} \right\} e^{- \chi_{{ic}^{\rho \; z_{0}}}}}},} & {{{if}\mspace{14mu} z_{ib}} \leq 0} \end{matrix}\mspace{20mu} {with}{\phi_{i}\left( {\rho \; z_{0}} \right)}} = \left\{ {\begin{matrix} {{{\left\lbrack {\frac{3}{2} - {\phi_{i}(0)}} \right\rbrack {\frac{z_{0}}{{\overset{\_}{z}}_{i}}\left\lbrack {2 - \frac{z_{0}}{{\overset{\_}{z}}_{i}}} \right\rbrack}} + {\phi_{i}(0)}},} & {{{if}\mspace{14mu} z_{0}} < {\overset{\_}{z}}_{i\; \theta}} \\ {{\frac{3}{2}\left\{ {{\left\lbrack \frac{z_{0} - {\overset{\_}{z}}_{i}}{z_{im} - {\overset{\_}{z}}_{i}} \right\rbrack \left\lbrack {\frac{z_{0} - {\overset{\_}{z}}_{i}}{z_{im} - {\overset{\_}{z}}_{i}} - 2} \right\rbrack} + 1} \right\}},} & {{{if}\mspace{14mu} {\overset{\_}{z}}_{i}} \leq z_{0} \leq z_{im}} \\ 0 & {{{if}\mspace{14mu} z_{0}} > z_{im}} \end{matrix},} \right.} \right.}$ φ_(i)(0) being a value of a distribution of intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element, P_(i) an initial slope of the distribution of the intensities of the X-ray radiation generated at the surface of the object by the corresponding chemical element and determined by the relation ${P_{i} = \frac{g \cdot h^{4} \cdot \left( {F/\overset{\_}{R}} \right)^{2}}{\overset{\_}{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{im}} \right)}\rho \; z_{im}}},$ with ${{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{im}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{im}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{im}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{im}} \right)^{n}}} \right)}}}},$ χ_(ic) representing the mass absorption coefficient of the object for the corresponding chemical element ${{P_{i}^{\prime} = \frac{\left\lbrack {{\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack^{2} + {2P_{i}\rho \; {z_{0}\left\lbrack {{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}} \right\rbrack}}}{\rho \; {z_{0}\left\lbrack {{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}} - {2{\phi_{i}(0)}} - {P_{i}\rho \; z_{0}}} \right\rbrack}}},{P_{i}^{''} = {2\frac{{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)} - {\phi_{i}(0)}}{\rho \; z_{0}}}},{and}}\mspace{11mu}$ $\; {{z_{ib} = {z_{0}\frac{{2{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{0}} \right)}} - {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}{{P_{i}\rho \; z_{0}} + {\phi_{i}(0)} - {\phi_{i}\left( {\rho \; z_{0}} \right)}}}},}$ z_(im) a maximum ionization depth of the corresponding chemical element, ${{\overset{\_}{z}}_{i} = {{\overset{\_}{z}}_{ip}\frac{\rho_{i}}{\rho}{\frac{n}{n_{i}}\left\lbrack {1 + {0.048\left( {2.5 - \frac{E_{0}}{20}} \right)\left( {1 - {LnM}_{i} + \frac{\left( {LnM}_{i} \right)^{2}}{3}} \right)\left( {\frac{M_{c}}{M_{i}} - 1} \right)}} \right\rbrack}}},$ z _(ip) a thickness for which the atomic number correction term φ _(i) for the corresponding pure chemical element is a maximum, n and n_(i) parameters depending respectively on the mean atomic number of the object and on the atomic number of the corresponding pure element, ρ_(i) a density of the corresponding pure chemical element and M_(c) and M_(i) atomic masses of the object and of the corresponding pure chemical element, E₀ an initial energy of electrons of the electron beam, β_(i) a term making it possible to fit a maximum of the atomic number correction term, I_(igco) an intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the electron beam, ξ_(i) a zeta-factor associated with the corresponding chemical element, α a parameter depending on the mean atomic number Zc of the object at the level of the zone, n a parameter depending on the mean atomic number Zc of the object at the level of the zone.
 15. Method according to claim 1, wherein in the course of each cycle the intermediate value of the mass-thickness is modified according to the following formula ${{\rho \; z_{0}} = {\overset{\_}{\Theta}\cos \; {\theta\Sigma}_{i = 1}^{N}\xi_{i}\frac{{\overset{\_}{\chi}}_{i}I_{iec}}{{\overset{\_}{\phi}}_{i}}}},$ with N being a total number of chemical elements identified, i an index of the current chemical element studied, I_(iec) an intensity of the emergent X-ray radiation corresponding to the chemical element of index i, χ _(i) an absorption correction term calculated in the course of the cycle and corresponding to the chemical element of index i, ξ_(i) zeta-factor associated with the chemical element of index i, the atomic number correction term φ _(i) being calculated in the course of the cycle and corresponding to the chemical element of index i, Θ being an incidence correction term calculated in the course of the cycle.
 16. Method according to claim 1, wherein in the course of each cycle an intermediate value of concentration C_(ic) of each chemical element is calculated according to the following formula: ${C_{ic} = {\frac{\xi_{i}}{\rho \; z_{0}}\frac{{\overset{\_}{\chi}}_{i}I_{iec}}{{\overset{\_}{\phi}}_{i}}\overset{\_}{\Theta}\cos \; \theta}},$ with I_(iec) being a measured intensity of the emergent X-ray radiation of the corresponding chemical element, ρz₀ an intermediate mass-thickness value modified in the course of the cycle, χ _(i) an absorption correction term for the corresponding chemical element calculated in the course of the cycle, ξ_(i) a zeta-factor associated with the corresponding chemical element, the atomic number correction term φ _(i) being calculated in the course of the cycle for the corresponding chemical element, Θ an incidence correction term calculated in the course of the cycle.
 17. Method for studying an object comprising: dividing the object into several zones to be studied, implementing, for each zone, the method according to claim 1 with a view to determining the corresponding mass-thickness value and, for each element of the said zone, the corresponding concentration value.
 18. Method according to claim 1, wherein in the initialization step the intermediate value of the mass-thickness ρz₀ and the intermediate value of concentration C_(ic) of each chemical element identified is determined by considering that the intensity of the corresponding emergent X-ray radiation is equal to an intensity of the radiation generated in the object by the said corresponding chemical element.
 19. Method according to claim 3, wherein ${{f_{m}\left( E_{is} \right)} = \frac{{AE}_{is}^{m}}{\left( {R_{p}/S_{p}} \right)_{i}}},$ with (R_(p)/S_(p))_(i) being the ratio of backscattering coefficients R_(p) and of a stopping power S_(p) for the corresponding pure chemical element, and A and m being parameters determined by Monte-Carlo simulation and depending on the energy level for the corresponding chemical element.
 20. Method according to claim 2, wherein each step of calculating the atomic number correction term φ _(i) uses the following relation ${{{\overset{\_}{\phi}}_{i}\left( {\rho \; z_{\theta}} \right)} = \frac{1 + {\alpha \left( {\rho \; z_{\theta}} \right)}^{n}}{1 + {\frac{\alpha \; C_{ic}}{\xi_{i}I_{igco}}\frac{\left( {\rho \; z_{\theta}} \right)^{({1 + n})}}{\left( {1 + \frac{\beta_{i}}{\left( {\rho \; z_{\theta}} \right)^{n}}} \right)}}}},$ with I_(igco) an intensity per unit time of an X-ray radiation generated by the corresponding chemical element in the object considered to be opaque to the electron beam, ξ_(i) a zeta-factor associated with the corresponding chemical element, n a parameter depending on the mean atomic number Zc of the object at the level of the zone, α a parameter depending on the mean atomic number Zc of the object at the level of the zone, β_(i) a term making it possible to fit a maximum of the term φ _(i) and z_(θ) a thickness in the direction of incidence θ determined on the basis of the incidence correction terms Θ and Θ _(im) calculated in the course of the cycle. 